Planetary-motion engine

ABSTRACT

In a rotary-piston engine, the contour of a normal section of the piston is either a composite trochoid or a translated composite trochoid. Each vertex of the normal section is either a generating point of the trochoid or has the form of a circular arc whose center is the generating point of the trochoid and whose radius is a fixed distance. Thus all the edges of the piston slide continuously on the inside face of engine cavity. The piston describes a planetary motion about a point at the same time as it revolves around an origin. Thus the volume of the working chambers changes. The opening and closing of connecting ducts for gas exchange are controlled. The resulting engine has only rotating moving parts, and they are in complete balance. The engine has no constrictions on the minor axis of the contour. Thus the movement of combustion gases is not impeded near top dead center. The engine has a high compression ratio. Because the displacement of the working chambers changes slowly near top dead center, combustion is completed before expansion begins. Therefore the conditions for thermal efficiency, maximum expansion, and maximum pressure prior to expansion are fulfilled. A reciprocating engine can be formed from this rotary-piston engine by installing a reciprocating piston on the generating point of a composite trochoid, putting a cylinder together with the piston, and using a crank mechanism that exploits the reciprocating motion generated by the generating point.

This is a national phase filing of International Application Number PCTJP 00175 filed Feb. 20, 1992 claiming priority from Japanese patentapplication number 3-229863 filed Feb. 21, 1991.

BACKGROUND OF THE INVENTION

This invention relates to two embodiments of a planetary-motion engine,a rotary-piston engine and a reciprocating engine.

The internal combustion engines currently in use, in addition to the gasturbine engine, are the reciprocating engine and the Wankelrotary-piston engine.

The Wankel rotary-piston engine has many advantages, but it also has thefollowing disadvantages. First, in the Wankel rotary-piston engine, itis impossible to raise the compression ratio high enough to sustainDiesel-engine operation. Second, the Wankel rotary-piston engine has twoconstrictions located on the minor axis of the contour of the normalsection of the tubular cavity in the housing. These constrictions dividethe working chamber along the minor axis into two parts, a trailing sideand a leading side. Because of this division, when the engine cyclenears top dead center, the trailing side is compressed at the same timethe leading side is expanded. This imbalance results in a loss ofmechanical energy.

There is prior art that attempts to offer solutions to theabovementioned problems of the Wankel rotary-piston engine. JP, A,49-46009 (May 2, 1974, Swiss National Patent No. 012260/72) discloses arotary piston engine comprising: (a) a housing containing a tubularcavity, (b) parallel guide members fixed to the base of the tubularcavity, (c) an eccentric wheel with a pilot wheel installed between theparallel guide members, (d) a crankshaft in which the main shaft of theeccentric wheel is attached to the crank pin, (e) a rotating pistonattached to the eccentric wheel, and (f) only one gear train includingan outer gear fixed to the crank pin and an inner gear fixed to therotating piston.

In this rotary piston engine, as the crankshaft revolves, the pilotwheel slides between the parallel guide members at the same time as itreciprocates. The pilot wheel and the eccentric wheel each rotate ontheir own respective axes as they revolve around the crank pin. Thus, asthe crankshaft revolves, the vertex of the rotating piston describes acurve that determines the contour of the normal section of the tubularcavity.

Further, the following prior art appears in the international searchreport of this PCT application. JP, A, 60-39361 (March 1, 1985, JohnFenton, U.S.A.) discloses a rotary-piston engine comprising: (a) ahousing containing a tubular cavity, (b) an eccentric shaft which is aoutput shaft, (c) an eccentric ring attached to the eccentric shaft, (d)a rotating piston attached to the eccentric ring, (e) one gear pairconsisting of an outer gear fixed to the eccentric shaft and an innergear fixed to the inside of the eccentric ring, and (f) a second gearpair consisting of an outer gear fixed to the outside of the eccentricring and an inner gear fixed to the rotating piston.

In this rotary-piston engine, no gear is fixed to the housing. As aresult, the vertex of the rotating piston cannot describe the curve thatdetermines the contour of the normal section of the tubular cavity whenthe rotating piston is installed in the tubular cavity.

JP, A, 51-104110 (Sep. 14, 1976, Kimiaki Kusano, Japan) disclosesmaterials for the surface of the rotating piston of a Wankelrotary-piston engine.

In an internal combustion engine, the higher its expansion ratio, thehigher its thermal efficiency. To reach a high thermal efficiencyrequires a high expansion ratio. In other words, the engine mustcomplete combustion before beginning the expansion part of the cycle.However, in the case of the high-revolution internal combustion enginesnow in practical use, it is impossible to complete combustion either inthe reciprocating engine or in the Wankel rotary-piston engine. There issimply not enough time. Thus the expansion ratio substantiallydecreases, and the thermal efficiency is reduced.

OBJECTS AND SUMMARY OF THE INVENTION

An object of the present invention is to make a rotary-piston enginethat does not require a reciprocating mass, as such a mass reduces thepower-weight ratio.

A further object of the present invention is to make a rotary-pistonengine that has no constriction in the contour of the normal section ofthe tubular cavity in the housing,

Still a further object of the present invention is to make arotary-piston engine that has enough time to complete combustion beforebeginning the expansion part of the cycle.

Yet a further object of the present invention is to make a rotary-pistonengine with a compression ratio high enough to permit the use of dieselfuel.

Still another object of the present invention is to make a reciprocatingengine that is not impeded by a reciprocating mass.

To achieve these objects, the planetary-motion rotary-piston enginecomprises a housing, a crankshaft, an eccentric shaft, a rotatingpiston, at least two gear units, and a plurality of connecting ducts forgas exchange.

The housing contains a tubular cavity in the shape of a fightnoncircular cylinder, that is, a solid cylindrical body whose normalsection, though curved, is not a perfect circle. A normal section is asection that is perpendicular to the axis of the tubular cavity. Withinthe tubular cavity, the flat surfaces at both ends are the bases, andthe curved surface is the lateral face. Both bases and the lateral facetogether are the inside face.

As for the rotating piston, a normal section is a section perpendicularto the axis of rotation. Though a vertex is generally a point, in thisapplication a corner that consists of an arc rather than a point is alsoreferred to as a vertex.

A polyhedron is a solid body enclosed by polygons, which are thesurfaces of the polyhedron. The sides of the polygons are the edges ofthe polyhedron, and the vertices of the polygons are the vertices of thepolyhedron. If two surfaces of a polyhedron are parallel, and thepolyhedron's other surfaces are parallel to a single straight line, thepolyhedron is a prism. The parallel surfaces are the bases, the surfacesparallel to the single straight line are the lateral faces, and theintersection of two adjacent lateral faces is the lateral edge of theprism. Further, when the lateral edges of a prism meet its baseperpendicularly, the prism is a right prism.

Each lateral face of a right prism is flat, and each of its lateraledges is a straight line. In this application a fight prism can alsohave cylindrical lateral faces and lateral edges. In other words, if thesides of the normal section of a right prism are curved, the solid bodyis still a right prism, as it is also if the vertices of the normalsection of are arcs instead of points.

The curve that determines the contour of the normal section of thetubular cavity is either a composite trochoid or a translated compositetrochoid in which the composite trochoid has been translated in paralleloutwards a fixed distance along a line normal to the composite trochoidand the inner and outer envelopes of the family of curves of thecomposite trochoid have at least two points of osculation. Further, theouter envelope of the family of curves that determines the contour ofthe normal section of the rotating piston can also be the contour of thenormal section of the tubular cavity.

The composite trochoid is the locus of the generating point of aperitrochoid in combination with a hypotrochoid, provided two conditionsare met. The first condition is that the base circle of the peritrochoidbe fixed to the eccentric arm of the hypotrochoid, so that the basecircle of the peritrochoid and the rolling circle of the hypotrochoidare concentric. The second condition is that the eccentric arm of theperitrochoid be fixed to the generating arm of the hypotrochoid, so thatthe center of the rolling circle of the peritrochoid becomes thegenerating point of the hypotrochoid.

The crankshaft comprises a main shaft and a crank pin. The function ofthe crankshaft is equivalent to that of the eccentric arm of thehypotrochoid. The main shaft pierces through the two bases of thetubular cavity along its axis. When the diameter of the rolling circleof the hypotrochoid is longer than the radius of the base circle of thehypotrochoid, we can also use a crankshaft (an eccentric shaft) whosemain shaft pierces through its crank pin.

The eccentric shaft comprises an eccentric main shaft and an eccentricwheel. The function of the eccentric shaft is equivalent to that of thegenerating arm of the hypotrochoid and the eccentric arm of theperitrochoid. The eccentric main shaft is attached to the crank pin.

The rotating piston is attached to the eccentric wheel and has the shapeof a right prism whose bases slide continuously on the bases of thetubular cavity. Each vertex of the normal section of the rotating pistonis either the generating point of the composite trochoid or it has theform of a circular arc whose center is the generating point of thecomposite trochoid and whose radius is equal to fixed distance. Further,the composite trochoid can be the contour of the normal section of therotating piston.

A first gear unit consists essentially of a fixed gear fixed to the baseof the tubular cavity and a rolling gear fixed to the eccentric mainshaft. The gear unit can have at least one idle gear. The function ofthe fixed gear is equivalent to that of the base circle of thehypotrochoid. The function of the rolling gear is equivalent to that ofthe rolling circle of the hypotrochoid.

A second gear unit consists essentially of a fixed gear fixed to thecrank pin and a rolling gear fixed to the rotating piston. The gear unitcan have at least one idle gear. The function of the fixed gear isequivalent to that of the base circle of the peritrochoid. The functionof the rolling gear is equivalent to that of the rolling circle of theperitrochoid.

The connecting ducts make openings into the working chambers formed bythe inside face of the tubular cavity and the lateral faces of therotating piston. The rotary motion of the rotating piston controls theopening and closing of the connecting ducts for gas exchange.

From the above planetary-motion rotary-piston engine, we can deriveother planetary-motion engines.

One such engine comprises a composite trochoid in which the ratiobetween the radii of the hypotrochoid's base circle and rolling circleis 2:1 and the ratio between the radii of the peritrochoid's base circleand rolling circle is 2:3.

Another such engine comprises a composite trochoid in which the ratiobetween the radii of the hypotrochoid's base circle and rolling circleis 3:2 and the ratio between the radii of the peritrochoid's base circleand rolling circle is 1:2.

Finally, the above-mentioned planetary-motion reciprocating engine ischaracterized by installing a reciprocating piston on the generatingpoint of a composite trochoid or a translated composite trochoid, inwhich the composite trochoid has been translated in parallel a fixeddistance along a line normal to the composite trochoid; by putting acylinder together with the reciprocating piston; and by using a crankmechanism that exploits the reciprocating motion generated by thegenerating point of the composite trochoid or of the translatedcomposite trochoid. In this composite trochoid, the ratio between theradius of the hypotrochoid's base circle and the radius of its rollingcircle is 2:1, the ratio between the radius of the peritrochoid's basecircle and the radius of its rolling circle is 1:2, and the radius ofthe base circle of the peritrochoid is equal to the radius of therolling circle of the hypotrochoid.

The above crank mechanism comprises a crank case, a crankshaft, aneccentric shaft, a connecting member, and two gear units.

The crankshaft comprises a crank main shaft and a crank pin, and thefunction of the crankshaft is equivalent to the function of theeccentric arm of the hypotrochoid.

The eccentric shaft comprises an eccentric wheel and an eccentric mainshaft attached to the crank pin. The function of the eccentric shaft isequivalent to the function of the generating arm of the hypotrochoid andof the eccentric arm of the peritrochoid.

The connecting member connects the reciprocating piston to the eccentricwheel, and the big end of the connecting member is attached to theeccentric wheel so that the connecting member may revolve therearound.The axis of the revolution of the connecting member is the center of thebig end of the connecting member. The center of the small end of theconnecting member is the generating point of either the compositetrochoid or the translated composite trochoid, and the function of theconnecting member is equivalent to that of the generating arm of theperitrochoid. The reciprocating piston is fixed to the small end of theconnecting member.

One of the two gear units consists of a fixed gear attached to the crankcase and a rolling gear attached to the eccentric main shaft, or of afixed gear attached to the crank case, a rolling gear attached to theeccentric main shaft, and at least one idle gear. The function of thesefixed gears is equivalent to the function of the base circle of thehypotrochoid. The function of these rolling gears is equivalent to thefunction of the rolling circle of the hypotrochoid.

The other of the two gear units consists of a fixed gear attached to thecrank pin and a rolling gear attached to the big end of the connectingmember, or of a fixed gear attached to the crank pin, a rolling gearattached to the big end of the connecting member, and at least one idlegear. The function of these fixed gears is equivalent to the function ofthe base circle of the peritrochoid. The function of these rolling gearsis equivalent to the function of the rolling circle of the peritrochoid.

Briefly stated, in a rotary-piston engine, the contour of a normalsection of the piston is either a composite trochoid or a translatedcomposite trochoid. Each vertex of the normal section is either agenerating point of the trochoid or has the form of a circular arc whosecenter is the generating point of the trochoid and whose radius is afixed distance. Thus all the edges of the piston slide continuously onthe inside face of engine cavity. The piston describes a planetarymotion about a point at the same time as it revolves around an origin.Thus the volume of the working chambers changes. The opening and closingof connecting ducts for gas exchange are controlled. The resultingengine has only rotating moving parts, and they are in complete balance.The engine has no constrictions on the minor axis of the contour. Thusthe movement of combustion gases is not impeded near top dead center.The engine has a high compression ratio. Because the displacement of theworking chambers changes slowly near top dead center, combustion iscompleted before expansion begins. Therefore the conditions for thermalefficiency, maximum expansion, and maximum pressure prior to expansionare fulfilled. A reciprocating engine can be formed from thisrotary-piston engine by installing a reciprocating piston on thegenerating point of a composite trochoid, putting a cylinder togetherwith the piston, and using a crank mechanism that exploits thereciprocating motion generated by the generating point.

According to an embodiment of the invention, a planetary-motionrotary-piston engine comprises: a housing containing a tubular cavityshaped as a right noncircular cylinder, in which a curve that determinesa contour of a normal section of the tubular cavity is a compositetrochoid composed of a hypotrochoid and a peritrochoid; the compositetrochoid having a family of curves; the family of curves having an innerenvelope and an outer envelope with at least two points of osculation; acrankshaft, pierced through bases of the tubular cavity along its axis,the crankshaft being functionally equivalent to an eccentric arm of thehypotrochoid; an eccentric shaft, attached to a crank pin of the crankshaft, the eccentric shaft being functionally equivalent to a generatingarm of the hypotrochoid and to an eccentric arm of the peritrochoid; arotating piston, attached to an eccentric wheel of the eccentric shaft,shaped as a right prism whose bases slide continuously on the bases ofthe tubular cavity; each vertex of a normal section of the rotatingpiston being a generating point of the composite trochoid; a first gearunit comprising a first fixed gear fixed to the base of the tubularcavity, the first fixed gear being functionally equivalent to a basecircle of the hypotrochoid; and a first rolling gear fixed to a mainshaft of the eccentric shaft, the first rolling gear being functionallyequivalent to a rolling circle of the hypotrochoid; a second gear unitcomprising a second fixed gear fixed to the crank pin, the second fixedgear being functionally equivalent to a base circle of the peritrochoid;and a second rolling gear fixed to the rotating piston, the second fixedgear being functionally equivalent to a rolling circle of theperitrochoid; and connecting ducts for gas exchange whose opening andclosing are controlled by the rotating piston.

According to a feature of the invention, a planetary-motionreciprocating engine comprises: a reciprocating piston installed at agenerating point of a composite trochoid composed of a hypotrochoid anda peritrochoid; the hypotrochoid having a ratio between radii of a basecircle and a rolling circle of 2:1; the peritrochoid having a ratiobetween radii of a base circle and a rolling circle of 1:2; a radius ofthe rolling circle of the hypotrochoid being equal to a radius of thebase circle of the peritrochoid; a crank mechanism effective forexploiting a reciprocating motion generated by the generating point ofthe composite trochoid, the crank mechanism comprising a crankshaftfunctionally equivalent to an eccentric arm of the hypotrochoid; aneccentric shaft attached to a crank pin of the crank shaft, theeccentric shaft being functionally equivalent to a generating arm of thehypotrochoid and to an eccentric arm of the peritrochoid; a connectingmember connecting the reciprocating piston to an eccentric wheel of theeccentric shaft, the connecting member being functionally equivalent toa generating arm of the peritrochoid; a first gear unit comprising afirst fixed gear coaxial with a main shaft of the crank shaft, the firstfixed gear being functionally equivalent to the base circle of thehypotrochoid; and a first rolling gear fixed to a main shaft of theeccentric shaft, the first rolling gear being functionally equivalent tothe rolling circle of the hypotrochoid; a second gear unit comprising asecond fixed gear fixed to the crank pin, the second fixed gear beingfunctionally equivalent to the base circle of the peritrochoid; and asecond rolling gear fixed to a end of the connecting member, the secondrolling gear being functionally equivalent to the rolling circle of theperitrochoid; and a cylinder within which the reciprocating piston movesback and forth.

The above, and other objects, features and advantages of the presentinvention will become apparent from the following description read inconjunction with the accompanying drawings, in which like referencenumerals designate the same elements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a first embodiment of the presentinvention taken along the lines C1-C2 of FIG. 2.

FIG. 2 is a sectional view of a first embodiment of the presentinvention taken along the lines B1-B2 of FIG. 1.

FIG. 3 is a sectional view of a first embodiment of the presentinvention taken along the lines C1-C2 of FIG. 2.

FIG. 4 is a sectional view of a first embodiment of the presentinvention taken along the lines D2-D1 of FIG. 2.

FIG. 5 is a sectional view of a first embodiment of the presentinvention taken along the lines E1-E2 of FIG. 2.

FIG. 6 is a sectional view showing a second embodiment of the presentinvention.

FIG. 7 is a sectional view showing a third embodiment of the presentinvention.

FIG. 8 is a sectional view, taken along B1-B2 of FIG. 82, of a fourthembodiment of the present invention.

FIG. 9 shows the elementary geometric structure of the compositetrochoid in the first embodiment.

FIG. 10 shows the geometric relation between the composite trochoid andthe rotating piston in the first embodiment.

FIG. 11 shows the elementary geometric structure of the compositetrochoid in the second and third embodiments.

FIG. 12 shows the geometric relation between the composite trochoid andthe rotating piston in the second and third embodiments.

FIG. 13 and 14 show the elementary geometric structure of the fourthembodiment and the geometric relation between a counter weight and areciprocating piston.

FIGS. 15-26 show composite trochoids for different values of a, b, r, c,d, and β.

FIG. 27 shows the elementary geometric structure of the family of curvesof the composite trochoid.

FIGS. 28-37 show families of curves of the composite trochoid fordifferent values of a, b, r, c, d, and β.

FIGS. 38-40 show families of curves determining the contour of thenormal section of the rotating piston of the rotary-piston engine of thepresent invention.

FIG. 41 shows the family of curves determining the contour (thecircular-arc-shaped vertices and the straight lines connecting them) ofthe normal section of the rotating piston of the rotary-piston engine ofthe present invention.

FIGS. 42-59 show the cycle of operations of the first embodiment.

FIG. 42 shows the intake stroke at T.D.C. (top dead center).

FIG. 43 shows the intake stroke at 90° after T.D.C.

FIG. 44 shows the intake stroke at 180° after T.D.C.

FIG. 45 shows the intake stroke at B.D.C. (bottom dead center).

FIG. 46 shows the compression stroke at 180° before T.D.C.

FIG. 47 shows the compression stroke at 90° before T.D.C.

FIG. 48 shows the compression stroke at T.D.C.

FIG. 49 shows the expansion stroke at 90° after T.D.C.

FIG. 50 shows the expansion stroke at 180° after T.D.C.

FIG. 51 shows the expansion stroke at B.D.C.

FIG. 52 shows the exhaust stroke at 180° before T.D.C.

FIG. 53 shows the exhaust stroke at 90° before T.D.C.

FIG. 54 shows the expansion stroke at T.D.C.

FIG. 55 shows the expansion stroke at 18° after T.D.C.

FIG. 56 shows the expansion stroke at 36° after T.D.C.

FIG. 57 shows the expansion stroke at 54° after T.D.C.

FIG. 58 shows the expansion stroke at 72° after T.D.C.

FIG. 59 shows the expansion stroke at 90° after T.D.C.

FIGS. 60-69 show the cycle of operations of the second embodiment.

FIG. 60 shows the intake stroke at T.D.C.

FIG. 61 shows the intake stroke at 105° after T.D.C.

FIG. 62 shows the intake stroke at B.D.C.

FIG. 63 shows the compression stroke at 105° after B.D.C.

FIG. 64 shows the compression stroke at T.D.C.

FIG. 65 shows the expansion stroke at 105° after T.D.C.

FIG. 66 shows the expansion stroke at B.D.C.

FIG. 67 shows the exhaust stroke at 105° after B.D.C.

FIG. 68 shows the exhaust stroke at T.D.C.

FIG. 69 shows the intake stroke at 105° after T.D.C.

FIGS. 70-81 show the cycle of operations of the third embodiment.

FIG. 70 shows the compression stroke at T.D.C.

FIG. 71 shows the expansion stroke at 105° after T.D.C.

FIG. 72 shows the expansion stroke at B.D.C.

FIG. 73 shows the exhaust stroke at 105° after B.D.C.

FIG. 74 shows the exhaust stroke at T.D.C.

FIG. 75 shows the scavenging stroke at 105° after T.D.C.

FIG. 76 shows the scavenging stroke at B.D.C.

FIG. 77 shows the scavenging stroke at 105° after B.D.C.

FIG. 78 shows the scavenging stroke at T.D.C.

FIG. 79 shows the intake stroke at 105° after T.D.C.

FIG. 80 shows the intake stroke at B.D.C.

FIG. 81 shows the compression stroke at 105° after B.D.C.

FIG. 82 shows the fourth embodiment in a sectional view taken along thelines C1-C2 of FIG. 8.

FIG. 83 shows the family of curves of a composite trochoid having twoloops on its minor axis.

FIG. 84 shows the family of curves of a composite trochoid that has apoint of osculation between its outer envelope and its inner envelope.

FIG. 85 shows an example of the elementary geometric structure of aquasi-composite trochoid.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

For brevity, hereinafter the planetary-motion rotary-piston engine is"the rotary-piston engine" and the planetary-motion reciprocating engineis "the reciprocating engine".

Referring to FIGS. 9-12, a composite trochoid determines the contour ofthe normal section of the tubular cavity in the housing. The compositetrochoid is comprised of a hypotrochoid and a peritrochoid. A basecircle 25 with a radius a and a rolling circle 26 with a radius bgenerate the hypotrochoid. A base circle 27 with a radius e and arolling circle 28 with a radius ƒ generate the peritrochoid.

For the hypotrochoid, a fixed point R on the prolongation of radius b ofrolling circle 26 is the generating point of the hypotrochoid. Adistance OQ is the eccentric quantity of the hypotrochoid. A distance QRis the generating radius of the hypotrochoid. A segment OQ is theeccentric arm of the hypotrochoid. A segment QR is the generating arm ofthe hypotrochoid.

For the peritrochoid, a fixed point P on the prolongation of radius ƒ ofrolling circle 28 is the generating point of the peritrochoid. Adistance QR is the eccentric quantity of the peritrochoid, and adistance RP is the generating radius of the peritrochoid. A segment QRis the eccentric arm of the peritrochoid, and a segment RP is thegenerating arm of the peritrochoid.

Since base circle 27 and rolling circle 26 have a common center in pointQ on eccentric arm OQ of the hypotrochoid, base circle 27 and rollingcircle 26 are concentric. Rolling circle 26 is not fixed to point Q oneccentric arm OQ of the hypotrochoid. However, base circle 27 is fixedto point Q. Thus rolling circle 26 can rotate about Q on eccentric armOQ of the hypotrochoid and base circle 27 cannot.

According to the properties of a hypotrochoid, rolling circle 26 rotateson point Q on eccentric arm OQ at the same time as it revolves aroundthe origin O. Thus point Q on eccentric arm OQ of the hypotrochoid alsorevolves around the origin 0. As rolling circle 26 rotates on its ownaxis, base circle 27, fixed to point Q, revolves around origin 0 butdoes not rotate on its own axis. Here base circle 27 and rolling circle26 are concentric. As rolling circle 26 rotates on its own axis,generating point R of the hypotrochoid revolves around base circle 27.

Eccentric arm QR of the peritrochoid is fixed to generating arm QR ofthe hypotrochoid so that the center of rolling circle 28 becomesgenerating point R of the hypotrochoid. Thus, as rolling circle 26rotates on its own axis, center R of rolling circle 28 also revolvesaround base circle 27. Further, because base circle 27 and rollingcircle 28 generate the peritrochoid, rolling circle 28 rolls (ratherthan slides) along an external circumference of base circle 27,inscribing it, as rolling circle 26 rotates on its own axis. In acoordinate system with point Q as origin, point P therefore generatesthe peritrochoid as rolling circle 26 rotates about its own axis.

Center R of rolling circle 28 is the generating point of thehypotrochoid. In a coordinate system whose origin is point O, center Rof rolling circle 28 generates the hypotrochoid as rolling circle 26rotates about its own axis. Eccentric arm QR of the peritrochoid hassegment QR in common with generating arm QR of the hypotrochoid.Consequently a locus 29 of point P is comprised of the hypotrochoid andthe peritrochoid. Locus 29 is thus a composite trochoid whose generatingpoint is point P.

Thus the composite trochoid is the locus of generating point P of theperitrochoid in combination with the hypotrochoid, subject to thefollowing conditions. First, base circle 27 of the peritrochoid must befixed to eccentric arm OQ of the hypotrochoid so that base circle 27 ofthe peritrochoid and rolling circle 26 of the hypotrochoid beconcentric. Second, eccentric arm QR of the peritrochoid must be fixedto generating arm QR of the hypotrochoid so that the center of rollingcircle 28 of the peritrochoid becomes generating point R of thehypotrochoid.

Consequently, rolling circle 28 describes a planetary motion about pointQ at the same time as it revolves around origin O. Because each of thevertices of the normal section of the rotating piston is generatingpoint P on the prolongation of the radius of rolling circle 28, therotating piston describes a planetary motion about point Q at the sametime as it revolves around origin O.

If distance RP be k, the coordinates of generating point P(x,y) of thecomposite trochoid can be expressed as follows, provided β, the phaseangle of generating point P, is a constant.

    x=(a-b) cos Θ+(ƒ-e) cos Φ+k cos (γ+β)

    y=(a-b) sin Θ+(ƒ-e) sin Φ+k sin (γ+β)

From these equations,

    Φ=Θ+λ,

where

    λ=-aΘ/b,

or

    Φ=(1-a/b)Θ.

Also from these equations,

    γ=Θ+λ+τ.

Since

    τ=-eλ/ƒ

and

    λ=-aΘ/b

    τ=eaΘ/ƒb,

and

    γ=(1-a/b+ea/ƒb)Θ.

Therefore the coordinates of generating point P(x,y) become

    x=(a-b) cos Θ+(ƒ-e) cos (1-a/b)Θ+k cos {(1-a/b+ea/ƒb)Θ+β}y=(a-b) sin Θ+(f-e) sin (1-a/b)Θ+k sin {(1-a/b+ea/ƒb)Θ+β}.

If the ratio between a radius e of base circle 27 and a radius b ofrolling circle 26 be c, then e=cb. If the ratio between a radius ƒ ofrolling circle 28 and radius e of base circle 27 be n, then ƒ=ne.Further, when the radius of base circle 27 is equal to the radius ofrolling circle 26, if the radius of the rolling circle 28 be r, thenr=nb.

Substituting, ƒ=cr, or, ƒ-e=cr-cb, and 1-a/b+ea/ƒb=1-a/b+a/r.

If the ratio between k and radius ƒ of rolling circle 28 be d, thenk=dƒ, or k=dcr.

Substituting, the coordinates of the generating point P(x,y) of thecomposite trochoid can be expressed as

    x=(a-b) cos Θ+c(r-b) cos (1-a/b)Θ+dcr cos {(1-a/b+a/r)Θ+β}                               (1)

    y=(a-b) sin Θ+c(r-b) sin (1-a/b)Θ+dcr sin {(1-a/b+a/r)Θ+β}                               (2)

If the phase angle of point Q be βa and the phase angle of point R beβb, then equations (1) and (2) become, if βa and βb are constants:

    x=(a-b) cos (Θ+βb)+c(r-b) cos {(1-a/b)Θ+βb}+dcr cos {(1-a/b+a/r)Θ+β}                               (3)

    y=(a-b) sin (Θ+βa)+c(r-b) sin {(1-a/b)Θ+βb}+dcr sin {(1-a/b+a/r)Θ+β}                               (4)

Equations (1) and (2) describe, with reference to a, b, c, d, r, and β,different composite trochoids, representative examples of which areshown in FIGS. 15-26.

Where the translated composite trochoid is the contour of the normalsection of the tubular cavity in the housing, the coordinates ofgenerating point Ps(xs,ys), which was translated in parallel outwardsthe fixed distance t along a line normal to the composite trochoid, canbe expressed as follows, if the angle between the x-axis and the normalline at the generating point P(x,v) is ν.

    xs=(a-b) cos Θ+c(r-b) cos (1-a/b)Θ+dcr cos {(1-a/b+a/r)Θ+β}+t cos ν

    ys=(a-b) sin Θ+c(r-b) sin (1-a/b)Θ+dcr sin {(1-a/b+a/r)Θ+β}+t sin ν

where tan ν=-(dx/dΘ)/(dy/dΘ). In this case, the shape of the vertex ofthe normal section of the rotating piston becomes a circular arc whosecenter is generating point P of the composite trochoid and whose radiusis equal to fixed distance t. Consequently, the shape of the lateraledges of the rotating piston becomes cylindrical. Thus, as the rotatingpiston revolves, the line of contact between the cylindrical lateraledge of the rotating piston and the lateral face of the tubular cavitymoves continuously on the surface of the cylindrical lateral edge of therotating piston. Therefore this line of contact is not continually inthe same position on the cylindrical lateral edge of the rotatingpiston. These techniques are used in the Wankel rotary-piston engine.

There are no restrictions on the curves linking the vertices of thenormal section of the rotating piston so long as the lateral faces ofthe rotating piston do not collide with the lateral face of the tubularcavity.

The volume of the working chamber becomes the smallest possible when theinner envelope of the family of curves that determines the contour ofthe normal section of the tubular cavity is the contour of the normalsection of the rotating piston. Under these conditions the compressionratio increases, which is favorable. Thus we generally use the innerenvelope of the family of curves that determines the contour of thenormal section of the tubular cavity for the contour of the normalsection of the rotating piston. Therefore the curve determining thecontour of the normal section of the rotating piston becomes the innerenvelope of the family of curves of either the composite trochoid or ofthe translated composite trochoid.

Referring to FIG. 27, to examine the structure of the family of curvesof the composite trochoid, let the center of a circle 32 be the origin Rof an XY-coordinate system. Further, let circle 32 be a base circle anda circle 33 be a rolling circle. Rolling circle 33 and base circle 32generate a hypotrochoid in the XY-coordinate system.

In the XY-coordinate system, let the center of a circle 34 be point Q oneccentric arm RQ of the hypotrochoid so that circle 34 and circle 33 canbe concentric. Let circle 34 be a base circle. So that a circle 35 mayrotate about generating point O of the hypotrochoid, we place the centerof circle 35 on generating point O of the hypotrochoid and let it be arolling circle. Rolling circle 35 and base circle 34 generate aperitrochoid.

So that the origin of an xy-coordinate system may become generic point Oof the hypotrochoid in the XY-coordinate system, we fix thexy-coordinate system to rolling circle 35 of the peritrochoid in theXY-coordinate system. Then the origin of the xy-coordinate system istranslated in parallel to generating point O of the hypotrochoid in theXY-coordinate system. The xy-coordinate system rotates about genericpoint O following the rotation of rolling circle 35 of the peritrochoidin the XY-coordinate system. The family of curves of the compositetrochoid can be described with reference to the xy-coordinate system.

Let the coordinates of generating point O of the hypotrochoid in theXY-coordinate system be (Xo, Yo). Let the rotating angle of rollingcircle 35 of the peritrochoid in the XY-coordinate system be χ. Let thecoordinates of the generating point of the composite trochoid in thexy-coordinate system be (x,y). Then the coordinates (X,Y) of the familyof curves of the composite trochoid can be expressed as:

    X=Xo+x cos χ-y sin χ

    Y=Yo+x sin χ+y cos χ,

where

    Xo=(ƒ-e) cos (ω+π)+(a-b) cos (δ+π)

    Yo=(ƒ-e) sin (ω+π)+(a-b) sin (δ+π).

In the composite trochoid, the value of δ becomes

    δ=ω+σ.

Since σ=-ƒω/e, we get

    δ=(1-ƒ/e)ω

The value of χ becomes

    χ=ω+σ+ν

Since ν=-bσ/a, and σ=-ƒω/e, we get

ν=bƒω/ae, and

χ=(1-ƒ/e+bƒ/ae)ω.

Since e=cb and ƒ=cr,

ƒ-e=cr-cb,

δ=(1=r/b)ω, and

χ=(1-r/b+r/a)ω.

Therefore the coordinates (X,Y) of the family of curves of the compositetrochoid can be expressed as:

    X=Xo+x cos (1-r/b+r/a)ω-y sin (1-r/b+r/a)ω     (5)

    Y=Yo+x sin (1-r/b+r/a)ω+y cos (1-r/b+r/a)ω     (6)

where

Xo=-c(r-b) cos ω-(a-b) cos (1-r/b)ω

Yo=-c(r-b)sinω-(a-b) sin (1-r/b)ω

x=(a-b) cos Θ+c(r-b) cos (1-a/b)Θ+dcr cos {(1-a/b+a/r)Θ+β}

y=(a-b)sin Θ+c(r-b)sin(1-a/b)Θ+dcr sin{(1-a/b+a/r)Θ+β}

FIGS. 28-37 show representative families of curves of the compositetrochoid. The composite trochoid itself is shown with a thick line.

For the rotary-piston engine of the present invention to have workingchambers of variable volume, the rotating piston must have at least twolateral edges that continually slide along the lateral face of thetubular cavity. Therefore the outer envelope and the inner envelope ofthe family of curves of the composite trochoid must have at least twopoints of osculation, as shown in FIGS. 28-37. Thus all the compositetrochoids shown in FIGS. 15-26 can be used as the contour of the normalsection of the tubular cavity. When there are loops on the minor axis ofa composite trochoid, the outer envelope and the inner envelope of thefamily of curves of this composite trochoid have no point of osculation,as shown in FIG. 83. When the outer envelope and the inner envelope ofthe family of curves of a composite trochoid have only one point ofosculation, as shown in FIG. 84, the rotary-piston engine of the presentinvention cannot function.

Further, the family of curves (Xs,Ys) of the translated compositetrochoid also have envelopes. They can be expressed as:

    Xs=Xo+xs cos (1-r/b+r/a)ω-ys sin (1-r/b+r/a)ω

    Ys=Yo+xs sin (1-r/b+r/a)ω+ys cos (1-r/b+r/a)ω,

where

    xs=(a-b) cos Θ+c(r-b) cos (1-a/b)Θ+dcr cos {(1-a/b+a/r)Θ+β}+t cos ν,

    ys=(a-b) sin Θ+c(r-b) sin (1-a/b)Θ+dcr sin {(1-a/b+a/r)Θ+β}+t sin ν,

and

    tan ν=-(dx/dΘ)/(dy/dΘ).

Install an idle circle between a trochoid's base circle and its rollingcircle. The fixed point on the prolongation of the radius of the rollingcircle generates a locus as the idle circle rolls, not slides, along thecircumference of the base circle. Hereinafter a "quasi-compositetrochoid" is a composite trochoid having at least one idle circleinstalled between the base circle and the rolling circle.

Referring to FIG. 85, to obtain a composite trochoid in which the ratiobetween the radii of the base circle and the rolling circle of thehypotrochoid is 2:1 and the ratio between the radii of the base circleand the rolling circle of the peritrochoid is 2:3, a concentric idlecircle 36 is installed between base circle 25 and rolling circle 26 andboth concentric idle circle 41 and an idle circle 37 are installedbetween base circle 27 and rolling circle 28.

Referring to FIGS. 10 and 32, when the curve that determines the contourof the normal section of the rotating piston is a composite trochoid,the outer envelope of the family of curves that determines the contourof the normal section of the rotating piston can be the contour of thenormal section of the tubular cavity.

Referring to FIG. 27, let circle 32 be a base circle and circle 33 be arolling circle. Rolling circle 33 and base circle 32 generate ahypotrochoid. To make a circle 34 concentric with circle 33, let circle34 be a base circle whose center is point Q on eccentric arm RQ of thehypotrochoid. To make circle 35 rotate about generating point O of thehypotrochoid, let circle 35 be a rolling circle whose center isgenerating point O of the hypotrochoid. Rolling circle 35 and basecircle 34 generate a peritrochoid. Further, let the ratio of thegenerating radius of the peritrochoid and radius a of rolling circle 35be h. Then the generating radius of the peritrochoid is ha.

Therefore the coordinates of the generating point (ν,w) of a compositetrochoid with the above structure can be expressed as follows, providedβc, the phase angle of generating point (ν,w), is a constant:

ν=(ƒ-e)cos(ω+π)+(a-b)cos(δ+π)+ha cos(χ+βc+π)

w=(ƒ-e)sin(ω+π)+(a-b)sin(δ+π)+ha sin(χ+βc+π).

Similarly to the family of curves of the composite trochoid,

    ν=-c(r-b) cos ω-(a-b) cos (1-r/b)ω-ha cos {(1-r/b+r/a)ω+βc}

    w=-c(r-b) sin ω-(a-b) sin (1-r/b)ω-ha sin {(1-r/b+r/a)ω+βc}.

When we describe the composite trochoid generated by the generatingpoint (ν,w) in the plane fixed to rolling circle 28 of the compositetrochoid described by equations (1) and (2), we get the family of curves(x,y) of the above composite trochoid. Then this family of curves (x,y)can be expressed, provided βe, the phase angle of the above compositetrochoid, is a constant, as:

    x=(a-b) cos Θ+c(r-b) cos (1-a/b)Θ+θ cos γ-w sin γ                                                   (7)

    y=(a-b) sin Θ+c(r-b) sin (1-a/b)Θ+ν sin γ+w cos γ(8)

where

    γ=(1-a/b+a/r)Θ+βe.

FIGS. 38-40 show representative families of curves expressed byequations (7) and (8). The composite trochoid generated by thegenerating point (ν,w) is shown by a thick line.

The composite trochoid generated by the generating point (ν,w) can bethe contour of the normal section of the rotating piston, and the outerenvelope of the family of curves of this composite trochoid can be thecontour of the normal section of the tubular cavity.

When the shape of the vertex of the normal section of the rotatingpiston is a circular arc, in equations (7) and (8), when ν=dcr and w=0,equations (7) and (8) express the coordinates of generating point P ofthe composite trochoid expressed by equations (1) and (2). Referring toFIG. 10, when βe, equations (7) and (8) express the coordinates ofgenerating point P1; when βe=-2π/3, the coordinates of the generatingpoint P2; and, when βe=-4π/3, the coordinates of the generating pointP3.

Therefore the vertex of the normal section of the rotating piston canhave the shape of a circular arc whose center is generating point P ofthe composite trochoid expressed by equations (1) and (2). The outerenvelope of the family of curves that determines the circular-arc-shapedvertices of the normal section of the rotating piston can be the contourof the normal section of the tubular cavity. If the curves that link thecircular-arc-shaped vertices do not interfere with the outer envelope ofthe family of curves that determine the circular-arc-shaped vertices,there is no restriction on the curves linking the circular-arc-shapedvertices. FIG. 41 shows the family of curves that determine the contour,that is, the circular-arc-shaped vertices (whose radii are equal to t)and the straight lines connecting them, of the normal section of therotating piston.

Referring to FIGS. 1-5, 9, and 10, the first embodiment of the presentinvention is a rotary-piston engine with a housing that contains atubular cavity. The curve that determines the contour of the normalsection of the tubular cavity is either a composite trochoid or atranslated composite trochoid. If the latter, the composite trochoid hasbeen translated outwards in parallel a fixed distance. A rotating piston3 is inserted into the tubular cavity. All the edges of rotating piston3 slide continuously on the inside face of the tubular cavity. Thelateral faces of rotating piston 3 and the inside face of the tubularcavity form three working chambers. Each chamber's volume changes withtime. Connecting ducts for gas exchange consist of an intake duct 10 andan exhaust duct 11.

In the composite trochoid, the ratio between the radii of base circle 25and rolling circle 26 is 2:1. The ratio between the radii of base circle27 and rolling circle 28 is 2:3. Therefore the curve that determines thecontour of the normal section of the tubular cavity can be expressed inthe following parametric equations:

    x=(a-b) cos Θ+c(r-b) cos (-Θ)+dcr cos (Θ/3+β)

    y=(a-b) sin Θ+c(r-b) sin (-Θ)+dcr sin (Θ/3+β)

Though the rotary piston engine of the present invention can beconstructed for any value of β, the favorable values are β=nπ/3, where nis an arbitrary integer. The most favorable value is β=2nπ/3. FIGS. 15and 16 show the composite trochoids for β=0; FIG. 17, for β=π/3.

Referring to FIGS. 15 and 16, constrictions appear on the minor axis ofthe composite trochoid when the value of d decreases. Values of d thatdo not lead to constrictions on the minor axis of the composite trochoiddepend on the value of c. When c>1, the resulting composite trochoid isunsuitable for the rotary-piston engine of the present invention. Avalue of c that is too small leads to problems with mechanical strength.Conditions for constructing the rotary-piston engine of the presentinvention are most favorable when 1.0>c>0.6.

Referring to FIG. 15, for c=0.8, conditions are favorable when d>4.4.Referring to FIG. 16, for c=0.9, conditions are favorable when d>3.6.However, since high values of d are disadvantageous for constructing therotary-piston engine of the present invention, d must be selected tohave low values that are within the limits that eliminate constrictionson the minor axis of the composite trochoid. Also, d should be chosen sothat the inner envelope of the family of curves of the compositetrochoid does not interfere with base circle 25 of the compositetrochoid.

Referring to FIGS. 1-7, the lateral face of the tubular cavity in thehousing is a rotor housing 1 containing a tubular cavity with both endsopen. Each of the two bases of the tubular cavity in the housing is aflat side housing 2. Rotating piston 3 fits into the tubular cavity ofrotor housing 1. Side housings 2 are attached to both ends of thetubular cavity of rotor housing 1.

For the contour of the normal section of rotating piston 3 we generallyuse the inner envelope of the family of curves determining the contourof the normal section of the tubular cavity of rotor housing 1. Thusrotating piston 3 has the shape of a right prism with a quasi-trigonalnormal section. Each of the three vertices of the quasi-trigonal normalsection of rotating piston 3 is either a generating point (one of P1,P2, or P3 in FIG. 10) of the composite trochoid or it has the form of acircular are whose center is the generating point of the compositetrochoid and whose radius is equal to the fixed distance. The anglesbetween each two of the three vertices of the quasi-trigonal normalsection and the center of the quasi-trigonal normal section are all 120°. FIG. 28 shows the family of curves of the composite trochoid for β=0.

Consequently all three lateral edges of rotating piston 3 slidecontinuously on the lateral face of the tubular cavity of rotor housing1, and all the edges of the two bases of rotating piston 3 slidecontinuously on the inside face of side housings 2. The lateral face ofthe tubular cavity of rotor housing 1, the inside face of side housings2, and the lateral faces of rotating piston 3 form the three workingchambers, whose volume changes with time.

To keep the working chambers airtight, there are apex seals 13 attachedto the three lateral edges of rotating piston 3 and side seals 14attached to the edges of the two bases of rotating piston 3. Intake duct10 and exhaust duct 11 make openings through rotor housing 1 into theworking chamber. Further, an ignition plug 12 is installed in rotorhousing 1. Both intake duct 10 and exhaust duct 11 can be installed inside housing 2.

A crankshaft 4, consisting of a crank main shaft and a crank pin, is anoutput shaft. The axis of rotation of crankshaft 4 is the axis of thecrank main shaft. The crank main shaft pierces through side housings 2to be coaxial with the tubular cavity. The distance between the axis(origin O) of the crank main shaft and the axis (point Q) of the crankpin is equal to the eccentric quantity OQ of the hypotrochoid. Thefunction of crankshaft 4 is equivalent to the function of eccentric armOQ of the hypotrochoid.

A fixed gear 5 is fixed to side housing 2 to be coaxial with the tubularcavity. Fixed gear 5, an internal gear, is also coaxial with the crankmain shaft.

A rolling gear 6, attached to the crank pin, can rotate on the latter'saxis, with the axis of rolling gear 6 as the axis of rotation. Rollinggear 6, an external gear, is engaged with fixed gear 5. The geometricrelation between fixed gear 5 and rolling gear 6 is the same as therelation between the hypotrochoid's base circle 25 and its rollingcircle 26. As crankshaft 4 revolves, rolling gear 6 rotates on the axisof the crank pin at the same time as it revolves around the axis of thecrank main shaft.

An eccentric shaft 7 consists of an eccentric main shaft and aneccentric wheel. The eccentric main shaft is attached to the crank pinand can rotate on the latter's axis, with the axis of the eccentric mainshaft as the axis of rotation. The eccentric main shaft is fixed torolling gear 6 to be coaxial therewith. Therefore the axis of theeccentric wheel is the fixed point on the prolongation of the radius ofrolling gear 6 and the generating point (point R) of the hypotrochoid.

Here the distance between the axis (point Q) of the eccentric main shaftand the axis (point R) of the eccentric wheel is equal to the eccentricquantity QR of the peritrochoid and to the generating radius QR of thehypotrochoid. The function of eccentric shaft 7 is equivalent to thefunction of eccentric arm QR of the peritrochoid and to the function ofgenerating arm QR of the hypotrochoid.

A fixed gear 8 is fixed to the crank pin to be coaxial therewith. Fixedgear 8, an external gear, is coaxial with rolling gear 6.

A rolling gear 9 is attached to the eccentric wheel and can rotate onthe latter's axis, with the axis of rolling gear 9 as the axis ofrotation. Rolling gear 9, an internal gear, is engaged with fixed gear8. The geometric relation between fixed gear 8 and rolling gear 9 is thesame as that between the peritrochoid's base circle 27 and its rollingcircle 28.

Rotating piston 3 is fixed to rolling gear 9 to be coaxial therewith.Accordingly, each of the three vertices of the quasi-trigonal normalsection of rotating piston 3 is a fixed point on the prolongation of theradius of rolling gear 9 and generating point P of the compositetrochoid.

Therefore rotating piston 3 describes a planetary motion on the axis(point Q) of the crank pin at the same time as it revolves around theaxis (origin O) of the crank main shaft. This double motion changes thevolume of the working chambers and causes apex seal 13 to open and closeintake duct 10 and exhaust duct 11, thereby exchanging combustion gas inthe working chamber. Thus the operating cycle has four strokes: anintake stroke shown in FIGS. 42-45, a compression stroke shown in FIGS.46-48, a combustion/expansion stroke shown in FIGS. 49-51, and anexhaust stroke shown in FIGS. 52-53. The expansion pressure ofcombustion is converted into the rotary motion of crankshaft 4. Here theangular velocity of rotating piston 3 is 1/3 the angular velocity ofcrankshaft 4 and directed in the same direction.

FIGS. 42-53 show the operation of this embodiment after separatechanges, each of 90°, in the angle of crankshaft 4. FIG. 48 shows theengine after completion of the compression stroke. In this position wehave ignition and combustion. FIGS. 54-59 show the engine in theexpansion stroke after separate 18° changes in the angle of crankshaft4. Referring to FIGS. 54-59, the change in the volume of the workingchamber near top dead center is very slow.

Since the center of gravity of rotating piston 3 is at point R (see FIG.10), we install a counter weight symmetrically around point Q to cancelthe mass of rotating piston 3. Further, we install a new counter weightsymmetrically around origin O to cancel the sum of the masses of theabove counter weight and rotating piston 3. These counter weights bringthe moving parts of the engine into complete balance.

Referring to FIGS. 6, 11, and 12, the rotary-piston engine of the secondembodiment of the present invention differs from the first embodiment inthat the curve determining the contour of the normal section of thetubular cavity of rotor housing 1 is a composite trochoid in which theratio between the radii of base circle 25 and rolling circle 26 is 3:2,and the ratio between the radii of base circle 27 and rolling circle 28is 1:2.

These ratios imply that the parametric equations of the curvedetermining the contour of the normal section of the tubular cavity canbe expressed as

    x=(a-b) cos Θ+c(r-b) cos (-Θ/2)+dcr cos (Θ/4+β)

    y=(a-b) sin Θ+c(r-b) sin (-Θ/2)+dcr sin (Θ/4+β)

This second embodiment of the rotary-piston engine of the presentinvention can be made for all values of β. When β=nπ/2, the conditionsfor making this embodiment are favorable, provided that n is anarbitrary integer. When β=(2n+1)π/2, the conditions for making thisembodiment are the most favorable. FIG. 20 shows the composite trochoidfor β=π/2; FIG. 21, the composite trochoid for β=0.

Referring to FIG. 20, apices appear on the corners of the compositetrochoid when the value of d decreases. Values of d that do not giverise to such apices on the corners of the composite trochoid depend onthe value of c. When c is too small, we have problems with mechanicalstrength. Therefore the most favorable conditions for making thisembodiment of the rotary-piston engine of the present invention are when1.0>c>0.7.

Referring again to FIG. 20, for c=0.95, conditions are favorable whend>2.1. However, since conditions are disadvantageous for making thisembodiment when d takes on high values, d should have low values withincertain limits. These limits are that appendices not appear on thecorners of the composite trochoid and that the inner envelope of thefamily of curves of the composite trochoid does not interfere with basecircle 25 of the composite trochoid.

Referring to FIG. 32, in the second embodiment, rotating piston 3 hasthe shape of a right prism with an oval normal section having twovertices. Accordingly, the lateral face of the tubular cavity of rotorhousing 1, the inside face of side housings 2, and the lateral faces ofrotating piston 3 form two working chambers whose volume changes withtime. Here the angles between the two vertices of the oval normalsection and the center of the oval normal section are both 180°. Theangular velocity of rotation of rotating piston 3 is one-fourth theangular velocity of rotation of crankshaft 4, which rotates in the samedirection as rotating piston 3.

Referring again to FIG. 6, intake ducts 10 and exhaust ducts 11 makeopenings through rotor housing 1 into the working chambers. A rotaryintake/exhaust valve 20 is installed in both intake duct 10 and exhaustduct 11. Opening and closing of both intake duct 10 and exhaust duct 11are controlled by rotary intake/exhaust valve 20. Further, rotaryintake/exhaust valve 20 is controlled by the rotating motion of rotatingpiston 3.

The angular velocity of rotation of rotary intake/exhaust valve 20 isone-eighth the angular velocity of rotation of crankshaft 4, whichrotates in the opposite direction from rotary intake/exhaust valve 20.We can also use other types of valves, such as poppet valves, etc.,instead of rotary valves.

Except for the differences mentioned above, the structure of therotary-piston engine of the second embodiment is identical to thestructure of the rotary-piston engine of the first embodiment.

Because rotating piston 3 describes a planetary motion on the axis ofthe crank pin at the same time as it revolves around the axis of thecrank main shaft, the volume of the working chambers changes. Furtherrotary intake/exhaust valves 20 open and close both intake ducts 10 andexhaust ducts 11, thereby exchanging the combustion gas in the workingchamber. Thus the operating cycle has four strokes: an intake strokeshown in FIGS. 60-62, a compression stroke shown in FIGS. 63-64, acombustion/expansion stroke shown in FIGS. 65-66, and an exhaust strokeshown in FIGS. 67-68. The expansion pressure of combustion is convertedinto the rotary motion of crankshaft 4. FIGS. 60-69 show the cycle ofoperations after separate 105° changes in the angle of crankshaft 4.FIG. 64 shows the cycle of operation after completion of the compressionstroke. In this position we have both ignition and combustion.

When we use the same balancing techniques as in the first embodiment,the moving parts are in complete balance.

Referring to FIG. 7, the third embodiment differs from the rotary-pistonengine of the second embodiment in that scavenging ducts 23 are openedthrough rotor housing 1 into the working chamber.

Intake duct 10, exhaust duct 11, and scavenging ducts 23 make openingsthrough rotor housing 1 into the working chambers. A rotary intake valve22 is installed in intake duct 10; a rotary exhaust valve 21, in exhaustduct 11; and a rotary scavenging vane 24, in scavenging duct 23. Openingand closing of intake duct 10 is controlled by rotary intake valve 22;opening and closing of exhaust duct 11, by rotary exhaust valve 21; andopening and closing of scavenging duct 23, by rotary scavenging valve24. Rotary intake valve 22, rotary exhaust valve 21, and rotaryscavenging valve 24 are controlled by the rotation of rotating piston 3.

The angular velocity of rotation of rotary scavenging valve 24 isone-quarter the angular velocity of rotation of crankshaft 4, whichrotates in the opposite direction from rotary scavenging valve 24. Theangular velocity of rotation of both rotary intake valve 22 and rotaryexhaust valve 21 is one-quarter the angular velocity of rotation ofcrankshaft 4, which rotates in the same direction as both rotary intakevalve 22 and rotary exhaust valve 21.

Except for the above-mentioned differences, the structure of therotary-piston engine of the third embodiment is identical to thestructure of the rotary-piston engine of the second embodiment.

Because rotating piston 3 describes a planetary motion on the axis ofthe crank pin at the same time as it revolves around the axis of thecrank main shaft, the volume of the working chambers changes. Rotaryintake valve 22 opens and closes intake duct 10, rotary exhaust valve 21opens and closes exhaust duct 11, and rotary scavenging valve 24 opensand closes scavenging ducts 23. These openings and closings exchange thecombustion gas in the working chamber. Thus the operating cycle has fivestrokes: a combustion/expansion stroke shown in FIGS. 71-72, an exhauststroke shown in FIGS. 73-74, a scavenging stroke shown in FIGS. 75-78,an intake stroke shown in FIGS. 79-80, and a compression stroke shown inFIGS. 81 and 70. The expansion pressure of combustion is converted intothe rotary motion of crankshaft 4. FIGS. 70-81 show the cycle ofoperations after separate 105° changes in the angle of crankshaft 4.FIG. 70 shows the cycle of operation after completion of the compressionstroke. In this position we have ignition and combustion.

Referring to FIGS. 8, 13, 14, and 82, the fourth embodiment is areciprocating engine with a crank mechanism that exploits thereciprocating motion generated by the generating point of a compositetrochoid and eschews the crank mechanism of the reciprocating engines incurrent use.

Referring to FIGS. 8 and 82, we make a reciprocating working chamber byinstalling a reciprocating piston 17 on the generating point of acomposite trochoid and putting a cylinder 16 together with it. Then weinstall a crankcase 15 and a connecting member 38. We also install apoppet intake valve 18, a poppet exhaust valve 19, and an ignition plug12 in the top of cylinder 16. This structure differs from that of thereciprocating engines in current use by its crank mechanism. Its cycleof operations is identical with current reciprocating engines. In FIGS.8 and 82 the counter weights of FIG. 13 are omitted.

The fourth embodiment is a planetary-motion reciprocating engine using acrank mechanism that exploits the reciprocating motion generated by thegenerating point of a composite trochoid, instead of the crank mechanismof the reciprocating engines in use to-day.

The structure of the crank mechanism of this embodiment of theplanetary-motion reciprocating engine of the present invention isessentially identical with the structure consisting of rotating piston3, eccentric shaft 7, crankshaft 4, and the two gear units in the firstembodiment, except for the following characteristics.

(a) The ratio between the radius of the pitch circles of fixed gear 5and rolling gear 6 is 2:1. The ratio between the radius of the pitchcircles of fixed gear 8 and rolling gear 9 is 1:2. The radius of thepitch circle of rolling gear 6 is equal to the radius of the pitchcircle of fixed gear 8.

(b) Fixed gear 5 is fixed to crank case 15. The crank main shaft ofcrankshaft 4 is pierced through crank case 15 to make the crank mainshaft and fixed gear 5 coaxial.

(c) Connecting member 38 connects reciprocating piston 17 to theeccentric wheel of eccentric shaft 7. The big end of connecting member38 is attached to the eccentric wheel so that connecting member 38 mayrevolve therearound. Reciprocating piston 17 is fixed to the small endof connecting member 38. The center of the small end of connectingmember 38 is the generating point of either the composite trochoid orthe translated composite trochoid. The function of connecting member 38is equivalent to the function of generating arm RP of the peritrochoidshown in FIG. 13.

(d) Rolling gear 9 is not fixed to rotating piston 3. Rather rollinggear 9 is fixed to the big end of connecting member 38.

We now explain the reciprocating motion generated by the generatingpoint of a translated composite trochoid in which a composite trochoidhas been translated in parallel a fixed distance t along a line normalto the composite trochoid.

In the above composite trochoid we let the ratio between the radii ofbase circle 25 and rolling circle 26 be 2:1 and the ratio between theradii of base circle 27 and rolling circle 28 be 1:2. Further, let c=1,βa=0, and β=βb/2. Then the coordinates of the generating point of theabove composite trochoid can be expressed, using equations (3) and (4),as:

    x=b cos Θ+b cos (-Θ+βb)+dr cos (βb/2)

    y=b sin Θ+b sin (-Θ+βb)+dr sin (βb/4)

    As cos A+cos B=2 cos {(A+B)/2} cos {(A-B)/2}

and

    sin A+sin B=2 sin {(A+B)/2} cos {(A-B)/2},

the above equations become

x=2c cos (βb/2) cos {(2Θ-βb)/2}+dr cos (βb/2),

and

    y=2b sin (βb/2) cos {(2Θ-βb)/2}+dr sin (βb/2),

or

    x=cos (βb/2){2b cos (Θ-βb/2)+dr}           (9)

    y=sin (βb/2){2b cos (Θ-βb/2)+dr}           (10)

Therefore the coordinates of the generating point of the translatedcomposite trochoid can be expressed as ##EQU1##

Therefore the coordinates of the generating point of the translatedcomposite trochoid can be expressed as ##EQU2##

In other words, the coordinates of the generating point of thetranslated composite trochoid can be expressed basically as

    xs=2b cos (Θ-βb/2)+dr

    ys=t,

and the angle formed by the prolongation of the translated compositetrochoid and the x-axis becomes βb/2.

Consequently the generating point of the translated composite trochoidgenerates a reciprocating motion whose tilt is βb/2, and the translatedcomposite trochoid becomes parallel to a straight line that passesthrough the origin O and has a tilt of βb/2. The interval between thisstraight line and the translated composite trochoid becomes t. Thedisplacement of the translated composite trochoid becomes a cosinefunction of the variable Θ with amplitude 2b. When the generating pointof the translated composite trochoid generates the reciprocating motion,the point Q (the axis of the crank pin) accordingly revolves around theorigin 0 (the axis of the crank main shaft). Because of this, we can usethe reciprocating motion generated by the generating point of thetranslated composite trochoid for the crank mechanism of thereciprocating engines in use today.

If we let t=0, we get a composite trochoid whose generating pointgenerates a reciprocating motion. The prolongation of the compositetrochoid passes through the origin O, the angle formed by theprolongation of the composite trochoid and the x-axis becomes βb/2, andthe displacement of the composite trochoid becomes a cosine function ofthe variable Θ with amplitude 2b.

When the generating point of the composite trochoid generates thereciprocating motion, the point Q (the axis of the crank pin) revolvesaround the origin O (the axis of the crank main shaft). Thus thereciprocating motion generated by the generating point of the compositetrochoid may be substituted for the crank mechanism of the reciprocatingengines in use today. The conditions for making this inventedplanetary-motion reciprocating engine are most favorable when t=0.

Referring to FIG. 13, when we make this reciprocating working chamber ofthe present invention by installing reciprocating piston 17 ongenerating point P of the composite trochoid and by putting cylinder 16together with it, reciprocating piston 17 moves back and forth incylinder 16. This displacement of the working chamber becomes a cosinefunction of the crank angle Θ with stroke amplitude 2a. Here dr becomesthe length of the connecting rod of the reciprocating engines in usetoday. When t≠0, reciprocating piston 17 reciprocates on a straight lineparallel to the x-axis.

Referring again to FIG. 13, let the mass of reciprocating piston 17 beM1 and its particle be generating point P. Let the mass of a counterweight 30 be M2 and its particle be a point G. Let the mass of a counterweight 31 be M3 and its particle be a point Z. Point G and point R aresymmetric about point Q. Point Z is on the circumference of base circle25, and the phase angle between point Z and point Q is π.

Here we let the angular velocity of point Q be α and the time be t. ThenΘ=αt. Since βb=0, the coordinates of the particle of reciprocatingpiston 17 can be expressed from equations (9) and (10) as

    x1=2b cos αt+dr

y1=0.

Since dr=0 and βb=π, the coordinates of the particle of counter weight30 can be expressed from equations (9) and (10) as

x2=0

y2=2b sin αt.

The coordinates of the particle of counter weight 31 can be expressed as

x3=-a cos αt

y3=-a sin αt.

The total sum Ix of the inertial forces of the moving parts on thex-axis can be expressed as ##EQU3##

The total sum Iy of the inertial forces of the moving parts on they-axis can be expressed as ##EQU4##

To get the moving parts into complete balance, the total sums Ix and Iymust equal 0. Thus complete balance implies

b M1=b M2

a M3=b(M1+M2).

Assuming that reciprocating piston 17 has mass M1 and is installed atpoint R, installing counter weight 30 at point G cancels the effect ofmass M1. Further, installing counter weight 31 at point Z cancels thesum of mass M2 of counter weight 30 and mass M1 of reciprocating piston17. Then the total sum of the inertial forces of the moving partsbecomes 0. Thus the counter weight installations described abovecompletely balance the moving parts.

In these installations point G and point R need not be symmetric aboutpoint Q, point Z need not be on the circumference of base circle 25, andthe phase angle between point Z and point Q need not be π.

Referring to FIG. 14, we install reciprocating piston 17 of mass M1 atgenerating point P2. Since βb=π, the coordinates of the particle ofreciprocating piston 17 can be expressed from equations (9) and (10) as

x2=0

y2=2b sin αt+dr.

The total sum Ix can be expressed as ##EQU5##

The total sum Iy can be expressed as ##EQU6##

Once again, to get the moving parts into complete balance, the totalsums Ix and Iy must equal 0. Thus complete balance implies

    2b M1=a M3.

Assuming that two reciprocating pistons 17 are installed at point Q,installing counter weight 31 at point Z cancels the sum of the mass ofthe two reciprocating pistons 17. Then the total sum of the inertialforces of the moving parts becomes O Thus the counter weightinstallations completely balance the moving parts.

A reciprocating motion is thereby changed to a simple rotating motion.Because of this change, the inertial forces of the reciprocating motionbecome 0, and the impediment from the reciprocating masses becomes 0.

Although the engine of the fourth embodiment has the form of areciprocating engine, it is, mechanically speaking, essentially arotary-piston engine.

Since counter weight 31 can be exchanged for two reciprocating pistons,we can now make, according to the present invention, a reciprocatingengine that is, for example, a 90° V-type or a star-shaped four-cylinderreciprocating engine.

The above-mentioned embodiments are meant for illustration only and arenot intended to define the limits of this invention. Further, thepresent invention also encompasses slightly altered structures that donot differ from the principle of this invention, one of which is thefollowing.

In the above-described embodiments, the mechanism consisted of two gearunits, crankshaft 4, eccentric shaft 7, and rotating piston 3, fromwhose operation came the locus described by equations (1) and (2). Hereone of the two gear units consisted of fixed gear 5 and rolling gear 6;the other, of fixed gear 8 and rolling gear 9.

However, we can also obtain the locus described by equations (1) and (2)with a gear unit that consists of a fixed gear, a rolling gear, and atleast one idle gear.

For example, since λ=-aΘ/b, rolling gear 6 rotates in the oppositedirection from crankshaft 4 at an angular velocity of a/b of its angularvelocity of rotation. Then we can (not shown):

(a) Fix to crankshaft 4 the axis of rotation of a stacked idle gear,whose upper and lower gear are both external. We let both fixed gear 5and rolling gear 6 be external gears. We now make a gear unit consistingof this stacked idle gear, fixed gear 5, and rolling gear 6.

(b) Fix to crankshaft 4 the axis of rotation of a stacked idle gear,whose upper and lower gear are both external. We let both fixed gear 5and rolling gear 6 be internal gears. We now make a gear unit consistingof this stacked idle gear, fixed gear 5, and rolling gear 6.

(c) Fix to crankshaft 4 the axes of rotation of an even number of idlegears whose gears are external. We now make a gear unit consisting ofthe even number of idle gears, fixed gear 5, and rolling gear 6.

We can also replace, with one of the gear units described in (a)-(c)above, the gear unit consisting of fixed gear 8 and rolling gear 9. Inthis case, since τ=-eλ/ƒ, we can use one of these gear units so thatrolling gear 9 rotate in a direction opposite to that of eccentric shaft7 and at an angular velocity e/ƒ of that of eccentric shaft 7. We mustalso fix the axes of rotation of these idle gears to eccentric shaft 7.

In other words, a quasi-composite trochoid as shown in FIG. 85 can bethe contour of the normal section of the tubular cavity in the housing.

The engine of the present invention has the following advantages:

1. The rotary piston engine characterized by the composite trochoid inwhich the ratio between the radii of the hypotrochoid's base and rollingcircles is 2:1, and the ratio between the radii of the peritrochoid'sbase and rolling circles is 2:3:

(a) There are no reciprocating parts. The only moving parts are thoseparts that rotate. Thus the moving parts can be in complete balance.

(b) Because this rotary-piston engine has no constrictions on the minoraxis of the contour of the normal section of the tubular cavity in thehousing, the movement of combustion gas is not impeded near top deadcenter.

(c) The engine has a higher compression ratio than the Wankelrotary-piston engine.

(d) Because the displacement of the working chamber changes slowly neartop dead center, combustion is completed before expansion begins.Therefore the conditions for thermal efficiency, maximum expansion, andmaximum pressure before the beginning of expansion, are fulfilled.

(e) In the automobile Diesel engines in present use, a great amount offuel is injected into the working chamber in one instant during a veryshort combustion stroke. Because the time for combustion is very short,combustion continues even after the expansion stroke starts. Thus theexpansion ratio decreases substantially, with a concomitant decrease inthermal efficiency. Further, the chance for a reaction between the fueland the oxygen is also low. Consequently measures to prevent black smokewill be insufficient.

In the rotary-piston engine of the present invention, on the contrary,the displacement of the working chamber changes slowly near top deadcenter. Thus there is enough time for complete combustion. Because theshape of the working chamber is flat and the flat working chamber moveswith almost unchanged displacement along the inside face of the rotorhousing, in relation to the working chamber, the fuel injection valvemoves along the chamber wall. As we use a fuel injection valve with highatomization and high distribution, we can inject sequences of smallamounts of fuel from one end of the working chamber to the other. Inthis way we can spread the highly atomized fuel all over the workingchamber. Thus the chance for a reaction between the fuel and the oxygenincreases, and we can expect combustion to be completed before expansionbegins. Consequently we can expect a high thermal efficiency, andconditions for preventing black smoke are good. There is no need forgreat efforts to make penetration and atomization compatible.

(f) Since the displacement of the working chamber changes slowly neartop dead center, there is enough time for combustion. We can call thispart of the operating cycle a combustion stroke. Further, thedisplacement of the working chamber changes slowly from the end of theexhaust stroke to the beginning of the intake stroke, a period we cancall a scavenging stroke. Consequently we can make a six-stroke cyclerotary-piston engine with an intake stroke, a compression stroke, acombustion stroke, an expansion stroke, an exhaust stroke, and ascavenging stroke.

2. In the rotary-piston engine characterized by the composite trochoidin which the ratio between the radii of the hypotrochoid's base androlling circles is 3:2, and the ratio between the radii of theperitrochoid's base and rolling circles is 1:2:

There are no reciprocating parts. The rotating parts are the only partsthat move. Thus the moving parts can be in complete balance.

3. In the reciprocating engine characterized by installing areciprocating piston on the generating point of a composite trochoid ora translated composite trochoid, putting a cylinder together with thereciprocating piston, and using a crank mechanism that exploits thereciprocating motion generated by the generating point of the compositetrochoid or translated composite trochoid, the moving parts can be incomplete balance, and the impediment from the reciprocating massesdisappears. Since piston slap does not occur, we need no cross-head.Since the reciprocating piston is independent, the side thrust from theweight of the reciprocating piston disappears. For a huge ship engine,we can use a V-type reciprocating engine. As a result, the ship enginebecomes smaller, and the center of gravity of the ship is therebylowered, which improves the vessel's stability and seaworthiness.

Having described preferred embodiments of the invention with referenceto the accompanying drawings, it is to be understood that the inventionis not limited to those precise embodiments, and that various changesand modifications may be effected therein by one skilled in the artwithout departing from the scope or spirit of the invention as definedin the appended claims.

What is claimed is:
 1. A planetary-motion rotary-piston enginecomprising:a housing containing a tubular cavity shaped as a rightnoncircular cylinder having an axis, in which a curve that determines acontour of a normal section of the tubular cavity is a compositetrochoid composed of a hypotrochoid and a peritrochoid; said tubularcavity being bounded at each end by two side housings geometricallycorresponding to two bases of said light noncircular cylinder; thecomposite trochoid having a family of curves; said family of curveshaving an inner envelope and an outer envelope with at least two pointsof osculation; a crankshaft, pierced through said side housings of saidtubular cavity along said axis; an eccentric shaft, coaxially attachedto a crank pin of said crankshaft, said eccentric shaft moving as agenerating arm of said hypotrochoid and as an eccentric arm of saidperitrochoid; a rotating piston, shaped as a right prism having twobases, which bases slide continuously on said side housings of saidtubular cavity; a normal section of said rotating piston having at leasttwo vertices corresponding to a like number of said points ofosculation; each vertex of said normal section of said rotating pistonbeing a generating point of said composite trochoid; a first gear unitcomprising:a first fixed gear being an internal gear and coaxially fixedto a one of said side housings of said tubular cavity, said first fixedgear moving as a base circle of said hypotrochoid; a first rolling gearcoaxially fixed to said eccentric shaft, said first rolling gear movingas a rolling circle of said hypotrochoid; said first fixed gear and saidfirst rolling gear engaging each other; a second gear unit comprising:asecond fixed gear coaxially fixed to said crank pin, said second fixedgear moving as a base circle of said peritrochoid; a second rolling gearcoaxially fixed to said rotating piston, said second rolling gear movingas a rolling circle of said peritrochoid; said second fixed gear andsaid second rolling gear engaging each other; said generating point ofsaid composite trochoid being defined by a pair of parametric equations,x=(a-b)cos Θ+c(r-b)cos(1-a/b)Θ+dcr cos{(1-a/b+a/r)Θ+β} and y=(a-b)sinΘ+c(r-b)sin(1-a/b)Θ+dcr sin{(1-a/b+a/r)Θ+β}, where Θ is an angularvelocity of said crankshaft, (1-a/b)Θ is an angular velocity of saideccentric shaft, (1-a/b+a/r)Θ is an angular velocity of said rotatingpiston, (a-b) is equal to a distance between an axis of said crankshaftand an axis of said crank pin, c(r-b) is equal to a distance betweensaid crank pin axis and an axis of said second rolling gear, dcr isequal to a distance between said second rolling gear axis and a one ofsaid vertices of said normal section of said piston, and β is a constantand is equal to a phase angle of said generating point of said compositetrochoid; and connecting ducts for gas exchange whose opening andclosing are controlled by said rotating piston.
 2. A planetary-motionrotary-piston engine according to claim 1 in which a ratio between radiiof said base circle and said rolling circle of said hypotrochoid is 2:1,and a ratio between radii of said base circle and said rolling circle ofsaid peritrochoid is 2:3.
 3. A planetary-motion rotary-piston engineaccording to claim 1, in which a ratio between radii of said base circleand said rolling circle of said hypotrochoid is 3:2, and a ratio betweenradii of said base circle and said rolling circle of said peritrochoidis 1:2.
 4. A planetary-motion rotary-piston engine according to claim 1,in which said curve determining said contour of said normal section ofsaid tubular cavity is a translated composite trochoid, where saidcomposite trochoid has been translated in parallel outwards a fixeddistance along a line normal to said composite trochoid, and each ofsaid vertices of said normal section of said rotating piston is formedas a circular are whose center is said generating point of saidcomposite trochoid and whose radius is equal to said fixed distance. 5.A planetary-motion rotary-piston engine according to claim 4 in which aratio between radii of said base circle and said rolling circle of saidhypotrochoid is 2:1, and a ratio between radii of said base circle andsaid rolling circle of said peritrochoid is 2:3.
 6. A planetary-motionrotary-piston engine according to claim 4, in which a ratio betweenradii of said base circle and said rolling circle of said hypotrochoidis 3:2, and a ratio between radii of said base circle and said rollingcircle of said peritrochoid is 1:2.
 7. A planetary-motion rotary-pistonengine, comprising:a housing containing a tubular cavity shaped as aright noncircular cylinder having an axis; said tubular cavity beingbounded at each end by two side housings geometrically corresponding totwo bases of said right noncircular cylinder; a rotating piston, shapedas a right prism having two bases, which bases slide continuously onsaid side housings of said tubular cavity, in which a curve thatdetermines a contour of a normal section of said rotating piston is acomposite trochoid composed of a first hypotrochoid and a firstperitrochoid; said composite trochoid having a family of curves; saidfamily of curves having an inner envelope and an outer envelope with atleast two points of osculation; said outer envelope having a secondhypotrochoid and a second peritrochoid whereby a geometric relationshipbetween said second hypotrochoid and said second peritrochoid isidentical to a geometric relationship between said first hypotrochoidand said first peritrochoid; a curve determining a contour of a normalsection of said tubular cavity is said outer envelope of said family ofcurves; a crankshaft, pierced through said side housings of said tubularcavity along said axis; an eccentric shaft, coaxially attached to acrank pin of said crankshaft, said eccentric shaft moving as agenerating arm of said second hypotrochoid and as an eccentric arm ofsaid second peritrochoid; said normal section of said rotating pistonhaving at least two vertices corresponding to a like number of saidpoints of osculation; a first gear unit comprising: a first fixed gearbeing an internal gear and coaxially fixed to a one of said sidehousings of said tubular cavity, said first fixed gear moving as a basecircle of said second hypotrochoid; a first rolling gear coaxially fixedto said eccentric shaft, said first rolling gear moving as a rollingcircle of said second hypotrochoid; said first fixed gear and said firstrolling gear engaging each other; a second gear unit comprising:a secondfixed gear coaxially fixed to said crank pin, said second fixed gearmoving as a base circle of said second peritrochoid; a second rollinggear coaxially fixed to said rotating piston, said second rolling gearmoving as a rolling circle of said second peritrochoid; said secondfixed gear and said second rolling gear engaging each other; said outerenvelope of said family of curves being defined by a first pair ofparametric equations, x=(a-b)cos Θ+c(r-b)cos(1-a/b)Θ+νcos γ-wsin γ andy=(a-b)sin Θ+c(r-b)sin(1-a/b)Θ+νsin γ+wcos γ, where γ=(1-a/b+a/r)Θ+βe,and ν and w define a second pair of parametric equations expressing saidcomposite trochoid, where ν=-c(r-b)cosω-(a-b)cos(1-r/b)ω-hacos{(1-r/b+r/a)ω+βc} and w=-c(r-b)sinω-(a-b)sin(1-r/b)ω-hasin{(1-r/b+r/a)ω+βc}, and where Θ is an angularvelocity of said crankshaft, (1-a/b)Θ is an angular velocity of saideccentric shaft, (1-a/b+a/r)Θ is an angular velocity of said rotatingpiston, (a-b) is equal to a distance between an axis of said crankshaftand an axis of said crank pin, c(r-b) is equal to a distance betweensaid crank pin axis and an axis of said second rolling gear, βe is aconstant and is equal to a phase angle of said rotating piston, ω is anangular velocity of an eccentric arm of said first hypotrochoid,(1-r/b)ω is an angular velocity of a generating arm of said firsthypotrochoid and also an angular velocity of an eccentric arm of saidfirst peritrochoid, (1-r/b+r/a)ω is an angular velocity of saidcomposite trochoid, ha is a generating radius of said compositetrochoid, and βc is a constant and is equal to a phase angle of agenerating point of said composite trochoid; and connecting ducts forgas exchange whose opening and closing are controlled by said rotatingpiston.
 8. A planetary-motion rotary-piston engine according to claim 7in which a ratio between radii of said base circle and said rollingcircle of said hypotrochoid is 2:1, and a ratio between radii of saidbase circle and said rolling circle of said peritrochoid is 2:3.
 9. Aplanetary-motion rotary-piston engine according to claim 7, in which aratio between radii of said base circle and said rolling circle of saidhypotrochoid is 3:2, and a ratio between radii of said base circle andsaid rolling circle of said peritrochoid is 1:2.
 10. A planetary-motionreciprocating engine comprising:a reciprocating piston installed at agenerating point of a composite trochoid composed of a hypotrochoid anda peritrochoid;said hypotrochoid having a ratio between radii of a basecircle and a rolling circle of 2:1; said peritrochoid having a ratiobetween radii of a base circle and a rolling circle of 1:2; a radius ofsaid rolling circle of said hypotrochoid being equal to a radius of saidbase circle of said peritrochoid; a crank mechanism effective forexploiting a reciprocating motion generated by said generating point ofsaid composite trochoid, said crank mechanism comprising:a crankshaftmoving as an eccentric arm of said hypotrochoid; an eccentric shaftcoaxially attached to a crank pin of said crankshaft, said eccentricshaft moving as a generating arm of said hypotrochoid and as aneccentric arm of said peritrochoid; a connecting member connected tosaid reciprocating piston, said connecting member moving as a generatingarm of said peritrochoid; a first gear unit comprising:a first fixedgear being an internal gear fixed to a crankcase and coaxial with saidcrank shaft, said first fixed gear moving as said base circle of saidhypotrochoid; a first rolling gear coaxially fixed to said eccentricshaft, said first rolling gear moving as said rolling circle of saidhypotrochoid; said first fixed gear and said first rolling gear beingengaged with each other; a second gear unit comprising:a second fixedgear coaxially fixed to said crank pin, said second fixed gear moving assaid base circle of said peritrochoid; a second rolling gear fixed to anend of said connecting member, said second rolling gear moving as saidrolling circle of said peritrochoid; said second fixed gear and saidsecond rolling gear being engaged with each other; and a cylinder withinwhich said reciprocating piston moves back and forth.
 11. Aplanetary-motion reciprocating engine according to claim 10, in whichsaid reciprocating piston is installed at a generating point of atranslated composite trochoid, where said composite trochoid has beentranslated in parallel a fixed distance along a line normal to saidcomposite trochoid.
 12. A planetary-motion rotary-piston engine,comprising:a housing containing a tubular cavity shaped as a rightnoncircular cylinder having an axis; said tubular cavity being boundedat each end by two side housings geometrically corresponding to twobases of said right noncircular cylinder; a rotating piston, shaped as aright prism having two bases, which bases slide continuously on saidside housings of said tubular cavity; at least two vertices of a normalsection of said rotating piston; each vertex of said normal section ofsaid rotating piston having a shape of a circular arc whose center is agenerating point of a composite trochoid composed of a hypotrochoid anda peritrochoid; a normal section of said tubular cavity being defined bya curve that is an outer envelope of a family of curves determining acontour of said normal section of said rotating piston; a crankshaft,pierced through said side housings of said tubular cavity along saidaxis; an eccentric shaft, coaxially attached to a crank pin of saidcrankshaft, said eccentric shaft moving as a generating arm of saidhypotrochoid and as an eccentric arm of said peritrochoid; a first gearunit comprising:a first fixed gear being an internal gear and coaxiallyfixed to a one of said side housings of said tubular cavity, said firstfixed gear moving as a base circle of said hypotrochoid; a first rollinggear coaxially fixed to said eccentric shaft, said first rolling gearmoving as a rolling circle of said hypotrochoid; said first fixed gearand said first rolling gear engaging each other; a second gear unitcomprising:a second fixed gear coaxially fixed to said crank pin, saidsecond fixed gear moving as a base circle of said peritrochoid; a secondrolling gear coaxially fixed to said rotating piston, said secondrolling gear moving as a rolling circle of said peritrochoid; saidsecond fixed gear and said second rolling gear engaging each other; saidgenerating point of said composite trochoid being defined by a pair ofparametric equations, x=(a-b)cos Θ+c(r-b)cos(1-a/b)Θ+dcrcos{(1-a/b+a/r)Θ+β} and y=(a-b)sin Θ+c(r-b)sin(1-a/b)Θ+dcrsin{(1-a/b+a/r)Θ+β}, where Θ is an angular velocity of said crankshaft,(1-a/b)Θ is an angular velocity of said eccentric shaft, (1-a/b+a/r)Θ isan angular velocity of said rotating piston, (a-b) is equal to adistance between an axis of said crankshaft and an axis of said crankpin, c(r-b) is equal to a distance between said crank pin axis and anaxis of said second rolling gear, dcr is equal to a generating radius ofsaid composite trochoid, and β is a constant and is equal to a phaseangle of said generating point of said composite trochoid; andconnecting ducts for gas exchange whose opening and closing arecontrolled by said rotating piston.